Secure information transfer based on global position

ABSTRACT

Secure communication of information is effected from a first party to a second party when the first party knows its own global location and the global location of the second party, and employs what essentially is an undiscoverable code signal that is broadcast to, and received by, both the first and the second parties. The first party securely communicates information to the second party by modifying the code signal with the information that is to be communicated and sends the modified code signal to the second party. Illustratively, the code signal is related to the Y component of a GPS signal.

RELATED APPLICATIONS

This is a continuation in part of U.S. patent application Ser. No.12/012,327, which was filed on Feb. 2, 2008.

BACKGROUND OF THE INVENTION

When information needs to be communicated in a secure manner onetypically turns to cryptographic techniques. It is generally recognizedthat with many cryptographic techniques the encrypted data can berecovered by an adversary, but only if the adversary has sufficientresources (e.g., computing power) and sufficient time. Most users aresatisfied when a method is secure “enough,” meaning that the time,effort, or expense to recover the data embedded in an encrypted messageis too great to make the data useful to an adversary.

With the above in mind, cryptographic techniques usually depend onencryption and decryption keys being in possession of the communicatingparties. Aside from the concern about the inherent security of messageencrypted with a particular method, the biggest concern is with thesecure creation, distribution and maintenance of the keys.

SUMMARY OF THE INVENTION

An advance in the art is achieved with a method that implements securetransmission of information from one party to another without the needfor cryptographic keys but, rather, based on unique geographicattributes such as position as well as time. More specifically, securecommunication of information is effected from a first party to a secondparty when the first party knows its own global location and the globallocation of the second party, and employs a code signal that isbroadcast to, and received by, both the first and the second parties.The first party securely communicates information to the second party bymodifying the code signal with the information that is to becommunicated and sends the modified code signal to the second party. Thecode signal that is received by the first party and is used to conveyinformation to the second party need not to be actually known to eitherof the parties, and from the standpoint of secure communication it isadvantageous for the broadcasted code signal (and the correspondingrelated received signals) to not be known to either of the parties andto be essentially impossible for the parties to discover. The signalthat is employed in the disclosed illustrative example is related to theY component of a GPS signal. Other wireless sources that are modified toinclude a signal like the Y component of the GPS signal can also beemployed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a first unit that securely transmits information withoutthe use of cryptographic keys;

FIG. 2 shows some of the processing within processor 40 of FIG. 1; and

FIG. 3 depicts some of the processing within a unit that receives thesignal transmitted by the FIG. 1 unit.

DETAILED DESCRIPTION

U.S. patent application Ser. No. 12/012,327 discloses an approachwhereby a first device, at location x, can verify an assertion by asecond device, at location y, as to the global position of the seconddevice. The disclosure presented an illustrative embodiment that isbased on the Global Positioning System (GPS) but the principlesdisclosed therein are broader and are not limited to the GPS. Forexamples, they can be readily applied to the other global navigationsatellite systems being developed and deployed worldwide.

To assist the reader in understanding the instant invention withouthaving to read the aforementioned application, the following repeats asignificant portion of the mathematical underpinnings presented in the12/012,327 application. It should be kept in mind that here, as well,the principles of the disclosed invention are broader than theillustrative example that uses the GPS.

FIG. 1 shows unit 100 that belongs to Remote Device B, whichsimultaneously receives a number of GPS satellite signals on frequencyL1, where the signal transmitted by satellite n can be expressed asS _(transmitted) ^(n) =A ^(n) D ^(n)(t)x _(C) ^(n)(t)cos(2π(f _(L1))t+φ₁)+B ^(n) D ^(n)(t)x _(Y) ^(n)(t)sin(2π(f _(L1))t+φ ₁)  (1)where D^(n)(t) is the data signal of satellite n, x_(C) ^(n)(t) is acode signal assigned to satellite n that is publicly known, x_(Y)^(n)(t) is a code signal assigned to satellite n that is not publiclyknown, f_(L1) is the frequency of the carrier, and φ₁ is the phase ofthe carrier relative to the beginning of the data and code signals. Unit100 is the party that wishes to send information to a remote unit 200without the use of cryptographic keys.

A GPS receiver receives a signal corresponding to the sum of the signalsof the individual satellites. The receiver can engage in the processingof signals as if all of the possible satellites are present but, ofcourse, some of the satellites are not within range of the GPSreceiver's antenna (i.e., not detectible) so the processing results forthose satellites are not viable. In other words, the signal arriving atthe FIG. 1 antenna corresponds to

$\begin{matrix}{{\sum\limits_{n = 1}^{K}\left\lbrack {{A^{''}{D^{''}(t)}{x_{C}^{''}(t)}{\cos\left( {{2{\pi\left( f_{L\; 1} \right)}t} + \varphi_{1}} \right)}} + {B^{''}{D^{''}(t)}{x_{Y}^{''}(t)}{\sin\left( {{2{\pi\left( f_{L\; 1} \right)}t} + \varphi_{1}} \right)}}} \right\rbrack} + {Noise}} & \left( {1a} \right)\end{matrix}$where K is the number of satellites that are within view of the antenna.

The following analysis follows the signal of only one satellite and, forsake of simplicity superscript n is omitted from the equations. The factthat other satellite signals exist is addressed later.

The transmitted signal is subjected to transit time delay beforereaching the receiver, and the signal that is received by a firstreceiver's antenna experiences a Doppler frequency shift, f_(D), due tothe satellite's movement in its orbit and possible receiver motion.Also, the transmitter and the receiver do not have a common clock, whichmeans that even when the transmitter and the receiver clocks are atidentical frequency, there is a phase difference between them. To makethe equations more general, one might assume that there is a time shift(the transitions are not fully aligned) between the AD(t)x_(C)(t) andthe BD(t)x_(Y)(t), so the signal received at the first receiver can beexpressed asS _(received,1) =A ₁ D(t−τ _(C,1))x _(C)(t−τ _(C,1))cos(2π(f _(L1) +f_(D,1))(t−τ ₁)+φ_(1,1))+B ₁ D(t−τ _(Y,1))x _(Y)(t−τ _(Y,1))sin(2π(f_(L1) +f _(D,1))(t−τ ₁)+φ_(1,1))  (2)or simplified toS _(received,1) =A ₁ D(t−τ _(C,1))x _(C)(t−τ _(C,1))cos(2π(f _(L1) +f_(D,1))t+φ _(1,1)−φ_(2,1))+B ₁ D(t−τ _(Y,1))x _(Y)(t−τ _(Y,1))sin(2π(f_(L1) +f _(D,1))t)+φ_(1,1)−φ_(2,1))  (3)It may be noted that for GPS, the C/A code and Y code are aligned, sothis generalization is not needed for a GPS-based embodiment.

As shown in FIG. 1, the received signal is detected and amplified inelement 10, conventionally downshifted in element 12 to a preselectedintermediate frequency (IF) by multiplying the received signal by signalsin(2π(f _(L1) −f _(IF))t+φ _(3,1))  (4)and low pass filtered by element 15. The signal of equation (4) isgenerated from reference oscillator 20 by frequency synthesizer 22,where φ₃ is the phase of the locally generated signal (relative to thebeginning of the data and code signals at the transmitting satellitewhich, of course, is unknown). The result at the output of the low passfilter isS _(downshifted,1) =A ₁ D(t−τ _(C,1))x _(C)(t−τ _(C,1))cos(2π(f _(IF) +f_(D,1))t+φ _(1,1)−φ_(2,1)−φ_(3,1))+B ₁ D(t−τ _(Y,1))x _(Y)(t−τ_(Y,1))sin(2π(f _(IF) +f _(D,1))t+φ _(1,1)−φ_(2,1)−φ_(3,1))  (5)or simplified toS _(downshifted,1) =A ₁ D(t−τ _(C,1))x _(C)(t−τ _(C,1))cos(2π(f _(IF) +f_(D,1))t+θ ₁)+B ₁ D(t−τ _(Y,1))x _(Y)(t−τ _(Y,1))sin(2π(f _(IF) +f_(D,1))t+θ ₁).  (6)

It may be noted that the above-described use of downshifting by use ofan IF modulator and low pass filter is illustrative, and that the A/Dcan be connected directly to the amplifier, and controlled to generate adigital signal as if it were downshifted as shown in FIG. 1.

As depicted, the output signal of the low pass filter is digitized inA/D converter 18 and applied to a combination of processor 40 andassociated memory 41, where the remainder of the processing takes place.

The processing in accord with the instant disclosure, shown in FIG. 2,begins with a carrier generator module 31 creating the signalcos(2π(f _(IF) +{circumflex over (f)} _(D))t+{circumflex over (θ)} ₁)−isin(2π(f _(IF) +{circumflex over (f)} _(D))t+{circumflex over (θ)}₁),(7)where {circumflex over (f)}_(D) is an estimate of the Doppler frequencyshift f_(D), and {circumflex over (θ)}₁ is an estimate of the phase θ₁.To be clear, the Doppler frequency shift and the phase estimates areestimates for a particular satellite. Multiplying the received (anddownshifted) signal of equation (6) by the phasor of equation (7) inelement 32 yields

$\begin{matrix}{{A_{1}{D\left( {t - \tau_{C,1}} \right)}{x_{C}\left( {t - \tau_{C,1}} \right)}\begin{Bmatrix}{+ {\cos\left( {{2{\pi\left( {f_{D,1} - {\hat{f}}_{D,1}} \right)}t} + \theta_{1} - {\hat{\theta}}_{1}} \right)}} \\{{+ i}\mspace{11mu}{\sin\left( {{2{\pi\left( {f_{D,1} - {\hat{f}}_{D,1}} \right)}t} + \theta_{1} - {\hat{\theta}}_{1}} \right)}}\end{Bmatrix}} + {B_{1}{D\left( {t - \tau_{Y,1}} \right)}{x_{Y}\left( {t - \tau_{Y,1}} \right)}\begin{Bmatrix}{+ {\sin\left( {{2{\pi\left( {f_{D,1} - {\hat{f}}_{D,1}} \right)}t} + \theta_{1} - {\hat{\theta}}_{1}} \right)}} \\{{- i}\mspace{11mu}{\cos\left( {{2{\pi\left( {f_{D,1} - {\hat{f}}_{D,1}} \right)}t} + \theta_{1} - {\hat{\theta}}_{1}} \right)}}\end{Bmatrix}}} & (8)\end{matrix}$which can be viewed as a real or inphase component (which is not shownin FIG. 2)S _(L1) =A ₁ D(t−τ _(C,1))x _(C)(t−τ _(C,1)){+cos(2π(f _(D,1)−{circumflex over (f)} _(D,1))t+θ ₁−{circumflex over (θ)}₁)}+B ₁ D(t−τ_(Y,1))x _(Y)(t−τ _(Y,1)){+sin(2π(f _(D,1) −{circumflex over (f)}_(D,1))t+θ ₁−{circumflex over (θ)}₁)}  (9)and a quadrature component (which is shown in FIG. 2)S _(Q,1) =A ₁ D(t−τ _(C,1))x _(C)(t−τ _(C,1)){sin(2π(f _(D,1)−{circumflex over (f)} _(D,1))t+θ ₁−{circumflex over (θ)}₁)}−B ₁ D(t−τ_(Y,1))x _(Y)(t−τ _(Y,1)){cos(2π(f _(D,1) −{circumflex over (f)}_(D,1))t+θ ₁−{circumflex over (θ)}₁)}.  (10)Integrating this signal in element 33 over a preselected interval thatis long enough to filter out the 2 f_(IF) signal component yields

$\begin{matrix}{{\int{A_{1}{D\left( {t - \tau_{C,1}} \right)}{x_{C}\left( {t - \tau_{C,1}} \right)}\begin{Bmatrix}{{\cos\left( {{2{\pi\left( {f_{IF} + {\hat{f}}_{D,1}} \right)}t} + {\hat{\theta}}_{1}} \right)}{\cos\left( {{2{\pi\left( {f_{IF} + f_{D,1}} \right)}t} + \theta_{1}} \right)}} \\{{- i}\mspace{11mu}{\sin\left( {{2{\pi\left( {f_{IF} + {\hat{f}}_{D,1}} \right)}t} + {\hat{\theta}}_{1}} \right)}{\cos\left( {{2{\pi\left( {f_{IF} + f_{D,1}} \right)}t} + \theta_{1}} \right)}}\end{Bmatrix}}} + {\int{B_{1}{D\left( {t - \tau_{Y,1}} \right)}{x_{Y}\left( {t - \tau_{Y,1}} \right)}\begin{Bmatrix}{{\cos\left( {{2{\pi\left( {f_{IF} + {\hat{f}}_{D,1}} \right)}t} + {\hat{\theta}}_{1}} \right)}{\sin\left( {{2{\pi\left( {f_{IF} + f_{D,1}} \right)}t} + \theta_{1}} \right)}} \\{{- i}\mspace{11mu}{\sin\left( {{2{\pi\left( {f_{IF} + {\hat{f}}_{D,1}} \right)}t} + {\hat{\theta}}_{1}} \right)}{\sin\left( {{2{\pi\left( {f_{IF} + f_{D,1}} \right)}t} + \theta_{1}} \right)}}\end{Bmatrix}}}} & (11)\end{matrix}$which can be written as

$\begin{matrix}{{\int{A_{1}{D\left( {t - \tau_{C,1}} \right)}{x_{C}\left( {t - \tau_{C,1}} \right)}\begin{Bmatrix}{\cos\left( {{2{\pi\left( {{2f_{IF}} + f_{D,1} + {\hat{f}}_{D,1}} \right)}t} + \theta_{1} + {\hat{\theta}}_{1}} \right)} \\{+ {\cos\left( {{2{\pi\left( {f_{D,1} - {\hat{f}}_{D,1}} \right)}t} + \theta_{1} - {\hat{\theta}}_{1}} \right)}} \\{{- i}\mspace{11mu}{\sin\left( {{2{\pi\left( {{2f_{IF}} + f_{D,1} + {\hat{f}}_{D,1}} \right)}t} + \theta_{1} + {\hat{\theta}}_{1}} \right)}} \\{{+ i}\mspace{11mu}{\sin\left( {{2{\pi\left( {f_{D,1} - {\hat{f}}_{D,1}} \right)}t} + \theta_{1} - {\hat{\theta}}_{1}} \right)}}\end{Bmatrix}}} + {\int{B_{1}{D\left( {t - \tau_{Y,1}} \right)}{x_{Y}\left( {t - \tau_{Y,1}} \right)}{\begin{Bmatrix}{\sin\left( {{2{\pi\left( {{2f_{IF}} + f_{D,1} + {\hat{f}}_{D,1}} \right)}t} + \theta_{1} + {\hat{\theta}}_{1}} \right)} \\{+ {\sin\left( {{2{\pi\left( {f_{D,1} - {\hat{f}}_{D,1}} \right)}t} + \theta_{1} - {\hat{\theta}}_{1}} \right)}} \\{{+ i}\mspace{11mu}{\cos\left( {{2{\pi\left( {{2f_{IF}} + f_{D,1} + {\hat{f}}_{D,1}} \right)}t} + \theta_{1} + {\hat{\theta}}_{1}} \right)}} \\{{- i}\mspace{11mu}{\cos\left( {{2{\pi\left( {f_{D,1} - {\hat{f}}_{D,1}} \right)}t} + \theta_{1} - {\hat{\theta}}_{1}} \right)}}\end{Bmatrix}.}}}} & (12)\end{matrix}$

In accord with one implementation of the principles disclosed herein,unit 100 knows its own global position and it also knows the globalposition of a particular remote unit 200. Illustratively, unit 100 issituated on the roof of a corporate headquarters building in one city,and unit 200 is situated on the roof of a corporate building in anothercity. If unit 100 does not know the location of unit 200, it may obtainit from unit 200 and verify that the location is bona fide in the mannerdisclosed in the parent application identified above. Armed with thisknowledge, unit 100 is able to send information to unit 200 bygenerating and processing a signal that is a close facsimile of thesignal that unit 100 knows is received by unit 200. Specifically, unit100 may modulate its signal with a time delay (delay-based encoding), afrequency shift (frequency-based encoding), or both, in order to effectsecure information transmittal to unit 200. To realize frequency-basedencoding, unit 100 may proceed as follows: from readily availableinformation, unit 100 obtains a fairly good estimate of the Dopplerfrequency shift, {circumflex over (f)}_(D,2), of the signal arriving atthe unit 200 location from a particular satellite (which is a fairlygood estimate), generates a reference signal with this frequency inelement 35, frequency shifts that signal by a chosen frequency value,f_(datum) in element 36, to obtain a frequency {tilde over (f)}_(D,2)(i.e., {tilde over (f)}_(D,2)={circumflex over (f)}_(D,2)+f_(datum)),and thus creates the signalcos[2π(f _(IF) +{tilde over (f)} _(D,2))(t)+{circumflex over (θ)}₂ ]−isin[2π(f _(IF) +{tilde over (f)} _(D,2))(t)+{circumflex over(θ)}₂]  (13)that is applied to element 37. To realize delay-based encoding, unit 100may proceed as follows: element 37 multiplies the signal of equation(13) by the quadrature signal of equation (12), delays it by δ_(datum)in element 38, and outputs the signal

$\begin{matrix}{s_{Q,1,2,\delta} = {\begin{Bmatrix}{A_{1}{D\left( {t - \tau_{C,1} - \delta_{datum}} \right)}{x_{C}\left( {t - \tau_{C,1} - \delta_{datum}} \right)}\sin} \\\left\lbrack {{2{\pi\left( {f_{D,1} - {\hat{f}}_{D,1}} \right)}\left( {t - \delta_{datum}} \right)} + \theta_{1} - {\hat{\theta}}_{1}} \right\rbrack \\{{- B_{1}}{D\left( {t - \tau_{Y,1} - \delta_{datum}} \right)}{x_{Y}\left( {t - \tau_{Y,1} - \delta_{datum}} \right)}\cos} \\\left\lbrack {{2{\pi\left( {f_{D,1} - {\hat{f}}_{D,1}} \right)}\left( {t - \delta_{datum}} \right)} + \theta_{1} - {\hat{\theta}}_{1}} \right\rbrack\end{Bmatrix} \times 2\begin{Bmatrix}{\cos\left\lbrack {{2{\pi\left( {f_{IF} + {{\hat{f}}_{D,2}\left\lbrack \left\lbrack {\overset{\sim}{f}}_{D,2} \right\rbrack \right\rbrack}} \right)}\left( {t - \delta_{datum}} \right)} + {\hat{\theta}}_{2}} \right\rbrack} \\{{- i}\mspace{11mu}{\sin\left\lbrack {{2{\pi\left( {f_{IF} + {{\hat{f}}_{D,2}\left\lbrack \left\lbrack {\overset{\sim}{f}}_{D,2} \right\rbrack \right\rbrack}} \right)}\left( {t - \delta_{datum}} \right)} + {\hat{\theta}}_{2}} \right\rbrack}}\end{Bmatrix}}} & (14)\end{matrix}$which can be expressed more compactly as

$\begin{matrix}{s_{Q,1,2,\delta} = {\begin{Bmatrix}{A_{1}{D\left( {t - \tau_{C,1} - \delta_{datum}} \right)}{x_{C}\left( {t - \tau_{C,1} - \delta_{datum}} \right)}{\sin(\alpha)}} \\{{- B_{1}}{D\left( {t - \tau_{Y,1} - \delta_{datum}} \right)}{x_{Y}\left( {t - \tau_{Y,1} - \delta_{datum}} \right)}{\cos(\alpha)}}\end{Bmatrix} \times 2\left\{ {{\cos(\beta)} - {i\mspace{11mu}{\sin(\beta)}}} \right\}}} & (15)\end{matrix}$where

-   α=2π(f_(D,1)−{circumflex over    (f)}_(D,1))(t−δ_(datum))+θ₁−{circumflex over (θ)}₁-   and β=2π(f_(IF)+{tilde over (f)}_(D,2))(t−δ_(datum))+{circumflex    over (θ)}₂.

It might be remembered that the analysis above focuses on the signal ofone satellite while recognizing that signals from a number of satellitesare concurrently processed, and it also should be remembered that thesignal of equation (13) that is created within unit 100 pertains,relative to the Doppler shift and delay, to a single satellite that ischosen by unit 100. Thus, it should be realized that the equation (15)signal is really a sum of signals of the form found within the brackets{•} that are all multiplied by the 2{cos(β)−i sin(β)} term that isadjusted to parameters for the one chosen satellite; to wit, the outputsignal of unit 100, S₁₀₀, is

$\begin{matrix}{s_{100} = {2\left\{ {{\cos(\beta)} - {i\mspace{11mu}{\sin(\beta)}}} \right\}{\sum\limits_{n = 1}^{K}\begin{Bmatrix}{A_{1}^{''}{D^{''}\left( {t - \tau_{C,1} - \delta_{datum}} \right)}{x_{C}^{n}\left( {t - \tau_{C,1} - \delta_{datum}} \right)}{\sin\left( \alpha_{i} \right)}} \\{{- B_{1}^{''}}{D^{''}\left( {t - \tau_{Y,1} - \delta_{datum}} \right)}{x_{Y}^{n}\left( {t - \tau_{Y,1} - \delta_{datum}} \right)}{\cos\left( \alpha_{i} \right)}}\end{Bmatrix}}}} & \left( {15a} \right)\end{matrix}$where

-   α_(i)=2π(f_(D,1) ^((i))−{circumflex over (f)}_(D,1))(t−δ_(datum))+θ₁    ^((i))−{circumflex over (θ)}₁-   f_(D,1) ^((i)) is the Doppler of satellite i as measured at unit 100-   θ₁ ^((i)) is the phase shift of the signal from satellite i as    measured at unit 100.

Unit 100 sends the signal of equation (15a) to unit 200, which alsoreceives its own GPS signal, s₂. Within unit 200 signal s₂ isdownshifted to develop the signals ₂ ·s _(mix,2) =A ₂ D(t−τ _(C,2))x _(C)(t−τ _(C,2))cos[2π(f _(IF) +f_(D,2))t+θ′ ₂]+B ₂ D(t−τ _(Y,2))x _(P)(t−τ _(Y,2))sin[2π(f _(IF) +f_(D,2))t+θ′ ₂],  (16)where τ_(c,2), τ_(c,2) and f_(D,2) are the delays and Doppler frequencyshift experienced by the signal that reaches unit 200. It is noted thatin a conventional manner the Doppler frequency f_(D,2) may bedetermined, for example by tracking in a frequency-lock or phase-lockloop.

In accord with one embodiment of the principles disclosed herein anddepicted in FIG. 3, unit 200 receives a signal by means of elements thatcorrespond to elements 10, 12, 15, 18, 20 and 22 of FIG. 1, but whichare not shown in FIG. 2 for sake of clarity, and within the processor ofunit 200 (which corresponds to processor 40 of FIG. 1) performs whateffectively is a two-dimensional correlation between the signal receivedfrom the satellites and the signal received from unit 100, by shiftingthe signal received from the satellites (i.e., the signal of equation(16)) by f* in element 53, delaying the shifted signal by δ* in element54, multiplying the output of element 54 by the signal received fromunit 100 (i.e., the signal of equation (15) in element 55), integratingin element 56, and repeating the process with different values of f* andδ* to find a peak, all under management of controller 57.

The frequency shifting and the time delaying of the equation (16) signalyieldss _(2,δ) =A ₂ D(t−τ _(C,2)−δ*)x _(C)(t−τ _(C,2)−δ*)cos[2π(f _(IF)+

)(t−δ*)+θ′₂ ]+B ₂ D(t−τ _(Y,2)−δ*)x _(P)(t−τ _(Y,2)−δ*)sin[2π(f _(IF)+

)(t−δ*)+θ′₂]  (17)where

=f_(D,2)+f*. Labeling 2π(f_(IF)+

)(t−δ*)+θ′₂ as γ yieldss _(2,δ*) =A ₂ D(t−τ _(C,2)−δ*)x _(C)(t−τ _(C,2)−δ*)cos(γ)+B ₂ D(t−τ_(Y,2)−δ*)x _(P)(t−τ _(Y,2)−δ*)sin(γ).  (18)The multiplication of the equation (18) signal by the signal of equation(15) yields

$\begin{matrix}{{s_{Q,1,2,\delta} \cdot s_{2,\delta}} = {\begin{Bmatrix}{A_{1}{D\left( {t - \tau_{C,1} - \delta} \right)}{x_{C}\left( {t - {\tau_{C,1}\delta}} \right)}{\sin(\alpha)}} \\{{- B_{1}}{D\left( {t - \tau_{Y,1} - \delta} \right)}{x_{P}\left( {t - \tau_{Y,1} - \delta} \right)}{\cos(\alpha)}}\end{Bmatrix} \times 2\left\{ {{\cos(\beta)} - {i\;{\sin(\beta)}}} \right\} \times {\begin{Bmatrix}{A_{2}{D\left( {t - \tau_{C,2} - \delta^{*}} \right)}{x_{C}\left( {t - {\tau_{C,1}\delta^{*}}} \right)}{\sin(\gamma)}} \\{{+ B_{2}}{D\left( {t - \tau_{Y,2} - \delta^{*}} \right)}{x_{P}\left( {t - \tau_{Y,1} - \delta^{*}} \right)}{\cos(\gamma)}}\end{Bmatrix}.}}} & (19)\end{matrix}$Carrying out the multiplication, grouping terms, and dropping the termsinvolving cos(γ+β) and sin(γ+β) because subsequent integration acts aslow pass filtering, yields

$\begin{matrix}\begin{matrix}{{S_{Q,1,2,\delta} \cdot S_{2,\delta^{*}}} = {\left( {U - V} \right) \times \left( {W + {iX} + Y - {iZ}} \right)}} \\{= \left\{ {{UW} + {iUX} + {UY} - {iUZ} -} \right.} \\\left. {{VW} - {iVX} - {VY} + {iVZ}} \right\}\end{matrix} & (20)\end{matrix}$whereU=A ₁ D(t−τ _(C,1)−δ)x _(C)(t−τ _(C,1)−δ)sin(α)  (21)V=B ₁ D(t−τ _(Y,1)−δ)x _(Y)(t−τ _(Y,1)−δ)cos(α)  (22)W=A ₂ D(t−τ _(C,2)−δ*)x _(C)(t−τ _(C,2)−δ*)cos(γ−β)  (23)X=A ₂ D(t−τ _(C,2)−δ*)x _(C)(t−τ _(C,2)−δ*)sin(γ−β)  (24)Y=B ₂ D(t−τ _(Y,2)−δ*)x _(Y)(t−τ _(Y,2)−δ*)sin(γ−β)  (25)Z=B ₂ D(t−τ _(Y,2)−δ*)x _(Y)(t−τ _(Y,2)−δ*)cos(γ−β)  (26)

The signal of equation (19) is integrated for various values of thedelay δ* and frequency offset f* to develop

$\begin{matrix}{\begin{matrix}{S_{\delta,\delta^{*}} = {\int{S_{Q,1,2,\delta} \cdot S_{2,\delta^{*}}}}} \\{= {\int\left\{ {{UW} + {iUX} + {UY} - {iUZ} - {VW} - {iVX} - {VY} + {iVZ}} \right\}}}\end{matrix}.} & (27)\end{matrix}$

At this point it may be noted that although the signal of equation (18)shows the signal of one satellite, unit 200 actually develops a signalthat includes a contribution from all visible satellites. It can beshown that each of the integration results therefore may result in aplurality of peaks, but the one that pertains to the chosen satellite isthe peak with highest energy. The energy of this peak, relative to thepeaks for the other satellites commonly visible to units 100 and 200,may be further enhanced through signal processing; for example, with adirectional antenna or a beamsteering antenna array focused to enhancethe signal of the satellite of interest.

The Doppler frequency estimate {circumflex over (f)}_(D,1) is very closeto f_(D,1), and the expression θ₁ is very close to {circumflex over(θ)}₁ (as a result of the capture and tracking operations).Consequently, all terms containing the factor “U” (which includessin(α)≈α≈0) drop out. Also, the cos(α) can be replaced by 1. Likewise,it is noted that the code sequence x_(C) is orthogonal to the codesequence x_(Y) (meaning that following integration the sum of theirproduct is zero). Consequently, the “VW” and “VX” terms drop out.Additionally, the “V” term, which contains the cos(α) reduces toV=B₁D(t−τ_(Y,1)−δ)x_(Y)(t−τ_(Y,1)−δ), leavingS _(δ,δ*) =∫{−VY+iVZ}=−∫VY+i∫VZ.  (28)

As indicated above, the expression of equation (27) is evaluated fordifferent values of δ* and f* (effectively a two-dimensionalcorrelation), and values δ*_(best) and f*_(best) are found that yieldthe maximum magnitude; i.e.,

$\begin{matrix}{{{S_{\delta,\delta^{*}}❘_{\max}}}^{2} = {\max\left( {\left( {\int{{\Psi\left( {t,\delta^{*}} \right)}{\cos(\alpha)}{\sin\left( {\gamma - \beta} \right)}}} \right)^{2} + \left( {\int{{\Psi\left( {t,\delta^{*}} \right)}{\cos(\alpha)}{\cos\left( {\gamma - \beta} \right)}}} \right)^{2}} \right)}} & (29)\end{matrix}$where Ψ(t,δ*)=(B₁D(t−τ_(Y,1)−δ))(B₂D(t−τ_(Y,2)−δ*))x_(Y)(t−τ_(Y,1)−δ)x_(Y)(t−τ_(Y,2)−δ*).

When the approximations are good; that is, f_(D,1)≈{circumflex over(f)}_(D,1) and θ₁≈{circumflex over (θ)}₁ then cos(α)≈1, and reinstatingwhat γ and β stand for, and looking only within the brackets, we have

( ( ∫ Ψ ⁡ ( t , δ * ) ⁢ x Y ⁡ ( t - τ Y , 1 - δ )   ⁢ x Y ⁡ ( t - τ Y , 2 -δ * ) ⁢ sin ⁡ ( 2 ⁢ π ⁡ ( f D , 2 - f D , 2 ) ⁢ t + Γ ) )   +   ⁢ ( ∫ Ψ ⁢ ( t ,δ * ) ⁢ x Y ⁡ ( t - τ Y , 1 - δ ) ⁢ x Y ⁡ ( t - τ Y , 2 - δ * ) ⁢ cos ( 2 ⁢ π ⁡( f D , 2 - f D , 2 ) ⁢ t +   ⁢   Γ ) ) 2 ⁢ ) ( 30 )whereΓ=2π[(f _(IF) +{tilde over (f)} _(D,2))δ−(f _(IF)+

)δ*]+θ′₂−{circumflex over (θ)}₂. (31)

Under the assumption that the code and the data take on value of only +1or −1, and because the autocorrelation of x_(Y)(t) is close to zero atall but t=0, it follows that equation (29) is essentially 0 except when(−τ_(Y,1)−δ)=(−τ_(Y,2)−δ*), orδ=δ*_(best)−τ_(Y,1)+τ_(Y,2).  (32)at which point it degenerates to

S δ , δ * ⁢ ❘ max = ⁢ ( B 1 ⁢ B 2 ) 2 [ ( ∫ sin ⁡ ( 2 ⁢ π ⁡ ( f D , 2 - f ~ D, 2 ) ⁢ t + Γ ) ) 2 + ⁢ ( ∫ cos ⁡ ( 2 ⁢ π ⁡ ( f D , 2 - f ~ D , 2 ) ⁢ t + Γ )) 2 ] = ⁢ ( B 1 ⁢ B 2 ) 2 [ ( ∫ sin ⁡ ( 2 ⁢ π ⁡ ( Δ ⁢ ⁢ f ) ⁢ t + Γ ) ) 2 + ⁢ ( ∫cos ⁡ ( 2 ⁢ π ⁡ ( Δ ⁢ ⁢ f ) ⁢ t + Γ ) ) 2 ] ( 33 )where Δf=

−{tilde over (f)}_(D,2), which leads toΔf=(f _(D,2) −{circumflex over (f)} _(D,2))+(f* _(best) −f_(secret))  (34)

The peak in the value of S_(δ,δ*)|_(max) occurs when Δf is very small.Since the estimate {circumflex over (f)}_(D,2) is very close to f_(D,2),equation (34) degenerates to f_(secret)=f*, and that equation (33)reduces to:S _(δ,δ*)|_(max)=(B ₁ B ₂)².  (35)

What we have, then, is that when the transit delay and Doppler frequencyshift information derived from published tables, geometricconsiderations, etc. are accurate, the autocorrelation has a peak onlywhen

-   (a) equation (32) condition holds; i.e.,    δ_(datum)=δ*−τ_(Y,1)+τ_(Y,2), and-   (b) equation (34) condition holds; i.e., f_(datum)=f*.

Since unit 200 can compute the transit delay difference(τ_(Y,2)−τ_(Y,1)) using, for example, published tables describing thesatellite orbits, the δ_(datum) information injected into the signal byunit 100 is easily recovered at unit 200 (equation 32). Conversely, whenunit 100 wishes unit 200 to recover a particular value δ*, unit 100accounts for the transit delay difference and computes the δ_(datum)that it needs to send. Also, when δ_(datum)=0, equation (32) yields avalue that corresponds to (τ_(Y,1)−τ_(Y,2)), and from theabove-mentioned tables, unit 200 can determine the location of unit 100.

The same capability exists in connection with the frequencies, in thatinformation can be communicated from unit 100 to unit 200 via thef_(datum) value.

Going back to equation (12), it is noted that it includes a signalcomponent that is modulated by the x_(C) code, which is publicly known.The chip rate of the x_(C) code has a bandwidth of about 2 MHz. (2 MHzmain lobe).

Based on this observation, an alternative embodiment in accord with theprinciples disclosed herein passes the signal of equation (12) through abandstop filter that is adjusted to remove the publicly known x_(C)code-modulated component (alternatively one can pass the signal ofequations (13) or (14) through the bandstop filter). Passing the signalthough the such a filter alters the equation (15) signal tos _(Q,1,2,δ)=−2[B ₁ D(t−τ _(Y,1)−δ)x _(Y)(t−τ _(Y,1)−δ)cos(α)][cos(β)−isin(β)]  (36)but that does NOT change equation (28). The difference, of course, isthat the embodiment that includes the bandstop filter does not send asignal that includes a knowable signal component that perhaps might beused by an adversary, and yet accomplishes the same result as anembodiment that does not use the bandstop filter.

In yet another embodiment in accord with the principles disclosedherein, the signal that is processed by unit 100 and sent to unit 200can be the signal of just a selected subset of the visible satellites;perhaps just one of the satellites. Illustratively, this is accomplishedby having the input antenna of unit 100 be steerable, though other morecomplicated techniques that would work as well. Any of the known designsor techniques for creating a steerable antenna is acceptable. There arealso other techniques that may be used which work as well. This methodreduces the number of peaks that are achievable at an adversary unit, aswell as at unit 200, and further it obscures the satellite signal whichwas used for the delay-based and/or frequency-based encoding, makingreverse-engineering of the values of δ_(datum) and/or f_(datum)substantially harder (or impracticable) for an adversary.

The above embodiments do not specify the duration of the signal thatunit 100 sends to unit 200. A short duration results in a smallercorrelation peak. A smaller peak is more difficult to detect in thepresence of peaks that result from spurious signals (noise). It is,therefore, useful to limit the duration of the signal that unit 100sends.

The above discloses the notion that two pieces of information can besend by unit 100 to unit 200, in a secure manner, with each transmissionof a signal segment: one embedded in δ_(datum) and the other embedded inf_(datum). Data can be communicated continuously, of course, by sending{δ_(datum), f_(datum)}-tuples in successive frames.

It may be noted that although the above discloses the principles of thisinvention in connection with GPS signals, that is not a limitation ofthis invention. Alternate sources that can create signal like the Y codeinclude device that operate in a WiFi protocol, Blue tooth protocol,cellular telephony protocols, etc.

It may be further noted that the illustrative embodiment disclosed aboveis adapted to a situation where the location of unit 100 is known tounit 200.

1. A method executed by a first unit having a first antenna located at afirst location, which antenna is constructed to receive a signalcomprising a sum of constituent signal, each from a different source ofa plurality of sources, and each of the constituent signals containing acomponent that is modulated by a known code and a component that ismodulated by a code that is not publicly known and not known to saidmethod (secret code), for communicating a data signal of said first unitto a second unit having a second antenna at a second location that isknown to said method, which is associated with a second unit, comprisingthe steps of: processing said signal to remove a Doppler frequency shiftthat said signal experiences in arriving at said first antenna, therebycreating a signal A; processing signal A with said data signal expressedthrough time delay, frequency shift, or both, to form signal A′ creatinga signal B that corresponds to a signal that is expected to have beenreceived at said second antenna in response to a signal transmitted by aparticular one of said sources, and processing said signal B with saiddata signal expressed through time delay, frequency shift, or both, toform signal B′; creating a signal C that is a function of signal A′multiplied by signal B′; and sending signal C to said second unit. 2.The method of claim 1 where said sources are satellites, and signal B′corresponds to cos(β)−i sin(β), where β=2π(f_(IF)+{tilde over(f)}_(D,2))({tilde over (t)})+{circumflex over (θ)}₂, f_(IF) anintermediate frequency that said second unit employs in downshifting thesignal received by said second antenna, {tilde over(f)}_(D,2)={circumflex over (f)}_(D,2)+f_(datum) when said input data isexpressed through said frequency shift, {tilde over (t)}=t−δ_(datum)when said input data is expressed through said time delay, {circumflexover (f)}_(D,2) is an estimate of a Doppler frequency shift experiencedby a signal, received by said second antenna, arriving from saidparticular satellite, and {circumflex over (θ)}₂ is an offset phaseshift estimate.
 3. The method of claim 1, where bandwidth of thecomponents that are modulated by said known code is lower than bandwidthof the components that are modulated by said secret code, furthercomprising the step of passing signal C through a bandstop filter priorto sending the signal to said second unit to remove the components thatare modulated by said known code.
 4. The method of claim 1 where saidsources are satellites and said first antenna is constructed to receiveprimarily the signal of said particular satellite.
 5. The method ofclaim 1 where said data signal comprises frames and at least some of theframes carry different data.
 6. The method of claim 1 where said sourcesare satellites, and each of the satellites outputs a signalcorresponding toS _(sent) ^(k) =A ₁ ^(k) D ^(k)(t)x _(C) ^(k)(t)cos(2π(f _(L1))t+φ ₁^(k))+B ₁ ^(k) D ^(k)(t)x _(Y) ^(k)(t)sin(2π(f _(L1))t+φ ₁ ^(k)) andsignal A corresponds to S_(sent) ^(k) isS _(downshifted,1) ^(k) =A ₁ ^(k) D ^(k)(t−τ _(C,1) ^(k))x _(C)(t−τ_(C,1) ^(k))cos(2π(f _(D,1) ^(k) −{circumflex over (f)} _(D,1) ^(k))t+θ₁ ^(k)−{circumflex over (θ)}₁ ^(k))+B ₁ ^(k) D ^(k)(t−τ _(Y,1) ^(k))x_(Y)(t−τ _(Y,1) ^(k))sin(2π(f _(D,1) ^(k) −{circumflex over (f)} _(D,1)^(k))t+θ ₁ ^(k)−{circumflex over (θ)}₁ ^(k)), where superscript kdesignates a particular one of said sources, sin(2π(f_(L1))t+φ₁) is acarrier signal at frequency f_(L1) and phase φ₁, f_(IF) is anintermediate frequency that is lower than f_(L1) , f_(D,1) ^(k) isDoppler frequency shift experienced by said S_(sent) ^(k) signal inreaching said unit, {circumflex over (f)}_(D,1) ^(k) is an estimate off_(D,1) ^(k), x_(Y) ^(k) is an unknown pseudorandom signal that is notpublicly known, B₁ ^(k) is an amplitude measure of saidsin(2π(f_(L1))t+φ₁) signal, cos(2π(f_(L1))t+φ₁) is a carrier signal thatis orthogonal to sin(2π(f_(L1))t+φ₁), x_(C) ^(k) is a known pseudorandomsignal, A₁ ^(k) is an amplitude measure of said cos(2π(f_(L1))t+φ₁)signal. D^(k) is a digital data signal that modulates said x_(Y) ^(k)pseudorandom signal and also said x_(C) ^(k) pseudorandom signal,τ_(Y,1) ^(k) is related to transit time delay of the modulated x_(Y)^(k) pseudorandom signal, τ_(C,1) ^(k) is related to transit time delayof the modulated x_(C) ^(k) pseudorandom signal, θ₁ ^(k) is a phase thatis related to said phase φ₁, and to said transit time delay, and{circumflex over (θ)}₁ ^(k) is an estimate of θ₁ ^(k).
 7. The method ofclaim 6 where signal B corresponds tocos[2π(f _(IF)+

)t+{circumflex over (θ)} ₂ ^(j) ]−i sin[2π(f _(IF)+

)t+{circumflex over (θ)} ₂ ^(j)] where

={circumflex over (f)}_(D,2) ^(j)+f_(datum), {circumflex over (f)}_(D,2)^(j) is an estimate of a Doppler frequency shift experienced by thesignal sent by said selected one of said sources, designated bysuperscript j, in reaching said second antenna; {circumflex over (θ)}₂^(j) is an estimate of a phase shift that that is related to a phaseshift of a signal from said selected one of said sources when processedin said second unit; and f_(datum) is a data signal sought to becommunicated by said unit.
 8. The method of claim 7 where signal C isrelated toA ₁ ^(k) D ^(k)(t−τ _(C,1) ^(k)−δ_(datum))x _(C)(t−τ _(C,1)^(k)−δ_(datum))cos(2π(f _(D,1) ^(k) −{circumflex over (f)} _(D,1)^(k))(t−δ _(datum))+θ₁ ^(k)−{circumflex over (θ)}₁ ^(k))+B ₁ ^(k) D^(k)(t−τ _(Y,1) ^(k)−δ_(datum))x _(Y)(t−τ _(Y,1) ^(k)−δ_(datum))sin(2π(f_(D,1) ^(k) −{circumflex over (f)} _(D,1) ^(k))(t−δ _(datum))+θ₁^(k)−{circumflex over (θ)}₁ ^(k)) multiplied bycos[2π(f _(IF)+

)(t−δ _(datum))+{circumflex over (θ)}₂ ]−i sin[2π(f _(IF)+

)(t−δ _(datum))+{circumflex over (θ)}₂] and δ_(datum) is another datasignal sought to be communicated by said unit.
 9. A method executed by aunit having an antenna located at a second location, which antenna isconstructed to receive a signal from each of one or more sources,comprising the steps of: creating a signal D that is developed fromsignals received by said antenna, which includes a signal of apreselected one of said sources, and the signal from said preselectedone of said sources includes a component that is not publicly known andnot known to said method; receiving a signal E from another unit havingan antenna at a first location for receiving signals from said one ormore sources; integrating a signal related to a product of signals D andE and to a signal F for a preselected duration to obtain an integrationresult signal; and repeating the step of integrating, with differentvalues of said signal F, to identify a particular signal F that yields amaximum value for said integration result signal.
 10. The method ofclaim 9 where said signal F has a first data component and a second datacomponent.
 11. The method of claim 9 where said signal related to aproduct of signals D and E is either signal D multiplied by signal Ethat is modified by signal F, or signal E multiplied by signal D that ismodified by signal F.